Unable to receive emails but able to receive via webmail

I recently registered a domain and had my website hosting taken care of by the same company. I got cpanel access to control all my website issues including domain emails. All went well until I was unhappy with the website hosting. I moved the website hosting elsewhere and had my www A records pointed to new host. I continued to receive emails for a short while after which I can now only send emails outside but all emails directed to my email address give a 'DELAY NOTIFICATION' before eventually failing totally. Any ideas what I could have missed? My business solely depends on emails but I cannot see whether the people I send to would have replied or not
Please Help!!!! Desperate